---
title: "In a cathode-ray tube demonstration, a beam of electrons traveling at constant velocity enters a region of uniform magnetic field directed perpendicular to the beam’s direction of propagation. An observer notes that the magnetic field bends the trajectory of the electrons into a circular arc, yet independent measurements show that the speed and kinetic energy of the electrons remain strictly constant throughout the deflection. Which of the following statements provides the correct physical explanation for why the magnetic field deflects the electrons without changing their speed?"
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url: "https://nerd-notes.com/ubq/121237/"
date_modified: "2026-08-23T04:58:59+00:00"
---

# In a cathode-ray tube demonstration, a beam of electrons traveling at constant velocity enters a region of uniform magnetic field directed perpendicular to the beam’s direction of propagation. An observer notes that the magnetic field bends the trajectory of the electrons into a circular arc, yet independent measurements show that the speed and kinetic energy of the electrons remain strictly constant throughout the deflection. Which of the following statements provides the correct physical explanation for why the magnetic field deflects the electrons without changing their speed?

In a cathode-ray tube demonstration, a beam of electrons traveling at constant velocity enters a region of uniform magnetic field directed perpendicular to the beam's direction of propagation. An observer notes that the magnetic field bends the trajectory of the electrons into a circular arc, yet independent measurements show that the speed and kinetic energy of the electrons remain strictly constant throughout the deflection. Which of the following statements provides the correct physical explanation for why the magnetic field deflects the electrons without changing their speed?

![A rectangular region containing a grid of six evenly spaced cross symbols arranged in two horizontal rows of three, labeled \vec{B} at the top right to indicate a uniform magnetic field directed into the page. A horizontal line with an arrowhead pointing to the right enters the region from the left, representing an electron with initial velocity \vec{v}. Inside the field region, the path curves downward into a circular arc. At a point along the circular arc, a tangent vector arrow pointing along the direction of motion is labeled \vec{v}, and a perpendicular vector arrow directed toward the center of curvature is labeled \vec{F}_B. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461138-NpOvEK.jpg)

- **A.** The magnetic force does positive work to accelerate the electrons perpendicular to their initial path, but this gain in energy is continuously offset by the energy dissipated through the induced magnetic field created by the moving charge beam.
- **B.** The magnetic force does work that continuously converts the electron's forward kinetic energy into transverse kinetic energy, leaving the total scalar kinetic energy invariant as the two velocity components trade magnitude.
- **C.** The uniform magnetic field exerts a constant-magnitude force that is perpendicular only to the magnetic field vector, causing the integrated work over each curved path segment to sum to zero.
- **D.** The magnetic force is defined by the vector cross product of velocity and magnetic field, ensuring the force is perpendicular to the instantaneous velocity at every point along the path so that the rate of work done on the electron is identically zero.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121237/*